A 60-kg woman is hospitalized for a severe, refractory asthma exacerbation. She is placed … — USMLE Step 3

A 60-kg woman is hospitalized for a severe, refractory asthma exacerbation. She is placed on a continuous intravenous infusion of aminophylline at a rate of 30 mg/hr. No initial loading dose was administered prior to starting the infusion.

Aminophylline has a known systemic clearance of 0.05 L/kg/hr and an elimination half-life of 6.93 hours in this patient population (assume $\ln(2) = 0.693$ ). The drug follows first-order kinetics and distributes into a single pharmacokinetic compartment.

After exactly 6.93 hours of continuous infusion, the patient's work of breathing abruptly increases, and an arterial blood gas analysis indicates impending respiratory failure. The intensivist decides to administer an immediate intravenous bolus (loading dose) of aminophylline to rapidly achieve the exact steady-state concentration that the current infusion rate is targeting.

What is the required intravenous bolus dose in milligrams?

Answer: 150 mg

Answer

The required intravenous bolus dose is 150 mg.

The correct bolus dose is 150 mg. First, the total clearance is found by multiplying the weight-based clearance by the patient's weight (

0.05 \text{ L/kg/hr} \times 60 \text{ kg} = 3 \text{ L/hr}

). The expected steady-state concentration (

C_{ss}

) achieved by this continuous infusion is the rate divided by the total clearance (

30 \text{ mg/hr} / 3 \text{ L/hr} = 10 \text{ mg/L}

). Because exactly one half-life (6.93 hours) has elapsed since the infusion started, the current plasma concentration has reached exactly 50% of the steady state, or 5 mg/L. The patient requires an additional 5 mg/L (

\Delta C

) to immediately achieve the target steady state. To convert this concentration deficit into a dose, the volume of distribution (

V_d

) must be determined. Using the fundamental pharmacokinetic relationship

t_{1/2} = (0.693 \times V_d) / Cl

, the

V_d

is calculated as

(6.93 \text{ hr} \times 3 \text{ L/hr}) / 0.693 = 30 \text{ L}

. Finally, the required bolus dose is the concentration deficit multiplied by the volume of distribution:

5 \text{ mg/L} \times 30 \text{ L} = 150 \text{ mg}

Step-by-Step Solution

Calculate the total systemic clearance (

Cl

Cl = 3.0 \text{ L/hr}

Clearance is provided per kilogram of body weight and must be multiplied by the patient's total weight to find the overall elimination capacity.

Calculate the target steady-state concentration (

C_{ss}

C_{ss} = 10 \text{ mg/L}

Steady-state concentration is the ratio of the continuous administration rate to the systemic clearance.

Determine the drug concentration at the time of clinical deterioration (6.93 hours).

C = 5 \text{ mg/L}

The time elapsed (6.93 hours) equals exactly one half-life. At one half-life, the drug accumulation reaches 50% of the ultimate steady-state concentration.

Calculate the volume of distribution (

V_d

V_d = 30 \text{ L}

The volume of distribution is necessary to calculate any bolus dose and is mathematically linked to half-life and clearance via the formula

V_d = (t_{1/2} \times Cl) / 0.693

Calculate the required bolus dose to reach the target

C_{ss}

Bolus = 150 mg

The bolus dose must only account for the remaining concentration deficit (

\Delta C

), which is multiplied by the volume of distribution.

Key Concept

Calculation of an immediate bolus dose during a continuous infusion by determining the deficit between the target steady-state concentration and the current plasma concentration based on the number of elapsed half-lives.

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